A227106 Numerators of harmonic mean H(n,3), n >= 0.

0, 3, 12, 3, 24, 15, 4, 21, 48, 9, 60, 33, 24, 39, 84, 5, 96, 51, 36, 57, 120, 21, 132, 69, 16, 75, 156, 27, 168, 87, 60, 93, 192, 11, 204, 105, 72, 111, 228, 39, 240, 123, 28, 129, 264, 45, 276, 141, 96, 147, 300, 17, 312, 159, 108, 165, 336, 57, 348, 177

Offset: 0

Author

Wolfdieter Lang, Jul 01 2013

Keywords

• nonn
• frac
• easy

Comments

a(n) = numerator(H(n,3)) = numerator(6*n/(n+3)), n>=0, with H(n,3) the harmonic mean of n and 3.

The corresponding denominators are given in A106619(n+3), n >= 0.

a(n+3), n>=0, is the third column (m=3) of the triangle A227041.

Examples

			The rationals H(n,3) begin: 0, 3/2, 12/5, 3, 24/7, 15/4, 4, 21/5, 48/11, 9/2, 60/13, 33/7, 24/5, 39/8, 84/17, 5, ...
		

Crossrefs

A227041(n+3,3), A106619(n+3) (denominator), n >= 0.

Programs

Mathematica

Table[Numerator[HarmonicMean[{n,3}]],{n,0,60}] (* Harvey P. Dale, Jun 01 2017 *)

Formula

a(n) = numerator(6*n/(n+3)), n >= 0.

a(n) = 6*n/gcd(n+3,6*n) = 6*n/gcd(n+3,18), n >= 0.